How to make this script compatible with Blender 2.8 API?
Here is the Script converted to 2.8
import bpy

def reset_shape_keys ():    
    for name, shape_key in get_active_block().items():
        shape_key.value = 0

def get_active_block ():
    block_id = bpy.context.object.active_shape_key.id_data.name
    return bpy.data.shape_keys[block_id].key_blocks

def select (selection):
    bpy.ops.object.select_all(action='DESELECT')
    selection.select_set(True)
    bpy.context.view_layer.objects.active = selection

def select_last_shape_key ():
    shape_key_count = len(get_active_block().items())
    bpy.context.object.active_shape_key_index = shape_key_count - 1

def remove_shape_keys (object):
    selection = bpy.context.object
    select(object)
    shape_key_count = len(get_active_block().items())
    select_last_shape_key()
    for i in range(0, shape_key_count):
        bpy.ops.object.shape_key_remove(all=False)
    select(selection)

def apply_modifiers (object):
    selection = bpy.context.object
    select(object)

    for key, modifier in object.modifiers.items():
        if key != 'Armature':
            bpy.ops.object.modifier_apply(apply_as='DATA', modifier=key)

    select(selection)        

def super_apply_modifiers ():
    original = bpy.context.object
    bpy.ops.object.duplicate_move()
    backup = bpy.context.object
    backup.name = 'backup'
    remove_shape_keys(original)
    apply_modifiers(original)

    for key, shape_key in get_active_block().items():
        select(backup)
        bpy.ops.object.duplicate_move()

        meshed_shape_key = bpy.context.object
        select(meshed_shape_key)
        reset_shape_keys()
        get_active_block()[key].value = 1
        bpy.ops.object.convert(target='MESH')

        select(original)
        meshed_shape_key.select_set(True)
        bpy.ops.object.join_shapes()
        select_last_shape_key()
        bpy.context.object.active_shape_key.name = key

        select(meshed_shape_key)
        bpy.ops.object.delete(use_global=False)

You can write the bpy.ops.object.duplicate_move() like this because your only use the default values of this operator.
[Tested on 2.83.3]